Binary Calculator
Perform binary arithmetic operations and convert between number systems with step-by-step solutions
Calculator
Binary Numbers
Operation
Number Systems Reference
Binary Arithmetic Rules
Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10
Multiplication
0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1
Number System Bases
Binary (Base 2):0, 1
Octal (Base 8):0-7
Decimal (Base 10):0-9
Hexadecimal (Base 16):0-9, A-F
Conversion Examples
1010₂ = 10₁₀ = A₁₆ = 12₈
1111₂ = 15₁₀ = F₁₆ = 17₈
11111111₂ = 255₁₀ = FF₁₆ = 377₈
Powers of 2
2⁰ = 1
2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
Frequently Asked Questions
Binary arithmetic follows the same principles as decimal arithmetic but uses only 0s and 1s. Addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (with carry). Subtraction uses borrowing from higher bits. Multiplication and division work similarly to decimal but are simpler since you only multiply/divide by 0 or 1.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.